FPGA Based Sensorless Control of a Permanent Magnet Synchronous Motor

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Degree project in

FPGA Based Sensorless Control of a Permanent Magnet Synchronous Motor

ALI EL HAFNI

Stockholm, Sweden 2012

XR-EE-E2C 2012:021 Electrical Engineering Master of Science

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Elektris he Antriebssysteme & Leistungselektronik

Te hnis he Universität Mün hen

Professor Dr.-Ing. Ralph Kennel

Master Thesis

FPGA Based Sensorless Control of a

Permanent Magnet Syn hronous Motor

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Ar isstraÿe21, 80333 Mün hen

Tel.: 089/28928358 Fax:089/28928336 email: eatei.tum.de

Ali El Hafni

FPGA Based Sensorless Control of a

Permanent Magnet Syn hronous Motor

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Magnet Syn hronous Motor

Lehrstuhl für

der Te hnis hen UniversitätMün hen

Submitted for the Degree of Master of S ien e, M.S .,

in Ele tri alPowerEngineering Engineering

Ali El Hafni

Born01.11.1986 inSaida, Lebanon

Supervision : Ms . Zhixun Ma

Beginning : 15.04.2012

End : 15.10.2012

Date of Presentation : 23.10.2012

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To Prof. Dr. Ing. Ralph Kennel, thank you for giving me the opportunity to

ondu t this proje t inone of the best universities in Europe. The experien ethat

I obtained during the lastsix monthis unforgettable.

To my supervisor Zhixun Ma, without your support and guidan e all the way,

thisproje twouldhavenotbeena hievable. Thankyouforbeingagreatsupervisor

and supporter, I have gained a lot of experien e working with you, in and outside

the s ope of the proje t. I hope I have been up to your expe tations. I wish you

su ess and lu k inyour resear h and life.

To my supervisor inKTH MatsLeksel, thank youfor being a greatmentorand

supervisor throughoutmy studiesinSto kholm, and givingme the han etotravel

abroadto work onthe proje t.

FinallyIwouldliketothankmyfriendsandfamily,andeveryone whosupported

mein this proje t.

Ali M. El Hafni

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Ar isstraÿe21, 80333 Mün hen

Tel.: 089/28928358 Fax:089/28928336 email: eatei.tum.de

MASTERTHESIS MA0019

Name of Student: ElHafni, Ali

S hanzenba hstrasse 8

81371,Mün hen

Interest of Study: Ele tri Power Engineering

Titleof Thesis : FPGA BasedSensorless Controlof a Permanent Magnet

Syn hronous Motor

Supervisor : Ms . Zhixun Ma

ProblemStatement

1. Study onsensorless ontrol of permanentmagnet syn hronous motors

2. Design and Simulationof anExtended KalmanFilterfor sensorless ontrol

3. FPGA Implementationof Extended Kalman Filterand high frequen y inje -

tion

Prof. Dr.-Ing. Ralph Kennel

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The work inthis thesis is based onresear h arriedout atthe Institute for Ele tri-

alDrive Systems and Power Ele troni s, Te hnis he Universität Mün hen (TUM)

supervised by Ms . Zhixun Ma. It is all my own work unless referen ed to the

ontraryin the text.

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Field Oriented Control (FOC) has proven to be a high performan e and robust

ontrol strategy for ele tri al drives. However the states of the ma hine, namely

speed and/or position, have to be measured in this ontrol strategy. Sin e the

useofen odersde reases therobustnessof thesystemand in reases ost,in reasing

interesthasbeenfo usedonsensorless ontrols hemes. This ontrolstrategyaimsto

eliminatetheen oder, andestimatethespeedand/orpositionofthema hinebased

only on the urrents and voltages measurements. In this thesis, sensorless ontrol

of a permanent magnet syn hronous ma hine (PMSM) is studied. Ttwo methods

are introdu ed inthis work. The ExtendedKalman Filterfor the high speed range

and the High Frequen y inje tion method for low speed range. In addition, these

methods are implemented using an FPGA instead of a DSP solution. Simulations

and experimental results are presented. The two methods prove to be ee tive in

their respe tive speed ranges, and provide a basis for hybrid full speed sensroless

ontroller.

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Fältvektorbaseradreglering(FieldOriented Control, FOC) har visatsigvara en ef-

fektiv o h robustkontrollstrategiför elektriskadrivsystem. Do k behöver mannor-

maltsetthatillgångtillhastigheto h/ellerpositionvidanvändningavdennametod.

Meneftersomanvändandetavrotationsgivareminskarrobusthetenhossystemeto h

ökarkostnaden har intressetför givarlös regleringökat. Vid givarlösreglering elim-

ineras rotationsgivaren o h hastigheten o h/eller positionen uppskattas baserat på

ström-o hspänningsmätningar. Idettaexamensarbeteundersökssensorlöskontroll

aven permanentmagnetiseradsynkronmaskin(PMSM). Tvåmetoderharstuderats.

Dels har det utökade Kalmanltret för den övre hastighetsområdet studerats o h

dels har en metod baserad på högfrekvensinjektionför det lägre hastighetsområdet

studerats. Metodernaharimplementeratsiett FGPA-baseratsystemiställetförett

system med DSP. Simuleringaro hexperimentellaresultat presenteras irapporten.

De två metoderna visar sig vara eektiva inom sina respektive hastighetsområden

o hutgörenutgångspunktförettsensorlösthybridkontrollsystemförhelahastighet-

sområdet.

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A knowledgement vii

Problem Statement ix

De laration xi

Abstra t xiii

1 Introdu tion 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Thesis Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Ba kground 5 2.1 Introdu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Review of Sensorless Control Te hniques . . . . . . . . . . . . . . . . 5

2.2.1 Fundamental Ex itationMethods . . . . . . . . . . . . . . . . 6

2.2.2 Salien yBased Methods . . . . . . . . . . . . . . . . . . . . . 8

2.2.3 Arti ialIntelligen e Methods . . . . . . . . . . . . . . . . . . 9

3 Sensorless Control Using Extended Kalman Filter 11 3.1 Introdu tion tothe Extended KalmanFilter . . . . . . . . . . . . . . 11

3.1.1 The Dis rete KalmanFilter . . . . . . . . . . . . . . . . . . . 11

3.1.2 The ExtendedKalman Filter . . . . . . . . . . . . . . . . . . 14

3.2 Extended Kalman Filterin Sensorless Control . . . . . . . . . . . . . 15

3.2.1 EKF inthe Stator Referen e Frame . . . . . . . . . . . . . . . 16

3.2.2 EKF inthe Rotating Referen eFrame . . . . . . . . . . . . . 19

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3.2.3 EKF in the RotatingReferen e Frame (SimpliedModel). . . 22

4 Sensorless Control Using Rotating High Frequen y Inje tion 25

4.1 Introdu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Con ept of Salien y BasedMethods . . . . . . . . . . . . . . . . . . . 26

4.3 RotatingHigh Frequen y Inje tion . . . . . . . . . . . . . . . . . . . 28

5 Model Based Design 31

5.1 Introdu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.2 Model-based designusing Matlab/Simulink. . . . . . . . . . . . . . . 32

5.3 FPGA Implementation of the EKF . . . . . . . . . . . . . . . . . . . 35

6 Results and Analysis 41

6.1 Extended KalmanFilter inthe stationary frame . . . . . . . . . . . . 41

6.2 EKF inthe rotatingframe . . . . . . . . . . . . . . . . . . . . . . . . 46

6.3 HighFrequen y Inje tion . . . . . . . . . . . . . . . . . . . . . . . . . 52

7 Con lusion 57

Bibliography 59

Appendix 64

A List of Symbols 65

B Per-unit system 67

C Fixed Point Data Type 69

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1.1 Field oriented ontrol. . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Sensorless ontrol te hniques [1℄. . . . . . . . . . . . . . . . . . . . . . 6

3.1 Extended Kalman Filterin sensorless ontrol. . . . . . . . . . . . . . 17

4.1 Salient polema hine [15℄. . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2 Magneti hysteresis loop[16℄. . . . . . . . . . . . . . . . . . . . . . . 28

4.3 High frequen y inje tion algorithm. . . . . . . . . . . . . . . . . . . . 30

5.1 Model based design inMatlab/Simulink[19℄ . . . . . . . . . . . . . . 34

5.2 FPGA-in-the-loopillustration[20℄. . . . . . . . . . . . . . . . . . . . 34

5.3 Blo k diagramof the EKF algorithm[12℄. . . . . . . . . . . . . . . . 35

5.4 Compensationblo kof the EKF. . . . . . . . . . . . . . . . . . . . . 36

5.5 Con ept of resour e sharing. . . . . . . . . . . . . . . . . . . . . . . . 38

6.1 EKF speed and position,in the stationaryframe, at500 rpm,with a step load at1s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6.2 EKF speed and position,in the stationaryframe, at200 rpm,with a step load at1s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.3 EKFspeedandposition,inthestationaryframe,atdierentreferen e speeds, with a onstant load. . . . . . . . . . . . . . . . . . . . . . . . 43

6.4 EKF speed and position, in the stationary frame, fpga-in-the-loop simulationat500 rpm, witha step load at 0.5s. . . . . . . . . . . . . 44

6.5 EKF speed and position, in the stationary frame, fpga-in-the-loop simulation,200 rpm to 600 rpm with a onstant load. . . . . . . . . . 44

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6.6 Estimated position and urrent using the Extended Kalman Filter

from-800 to-400 rpm, noload. . . . . . . . . . . . . . . . . . . . . . 46

6.7 Estimated position and urrent using the Extended Kalman Filter from-400 to-800 rpm, with load. . . . . . . . . . . . . . . . . . . . . 47

6.8 Estimated position and urrent using the Extended Kalman Filter from-400 to+800 rpm, noload. . . . . . . . . . . . . . . . . . . . . . 47

6.9 Estimated positionand urrentusingthe ExtendedKalmanFilterat -200rpm,noload. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.10 Estimated positionand urrentusingthe ExtendedKalmanFilterat -200rpm,with step load at 1s. . . . . . . . . . . . . . . . . . . . . . . 48

6.11 Estimated positionand urrentusingthe ExtendedKalmanFilterat -400rpm,with step load at 1.5s. . . . . . . . . . . . . . . . . . . . . . 49

6.12 EKF speed and positionsimulation at500 rpm inthe rotatingreferen e frame, with a step load at1s.. . . . . . . . . . . . . . . . . . . . 50

6.13 EKFspeedandpositionsimulationfordierentspeedsintherotating referen e frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.14 EKF speed and positionsimulation at500 rpm inthe rotatingreferen e frameusing the simplied model. . . . . . . . . . . . . . . . . . 51

6.15 Diagonal elements of the P matrix using the simpliedmodel. . . . . 51

6.16 Highfrequen y inje tion simulationat50 rpm. . . . . . . . . . . . . . 52

6.17 Highfrequen y inje tion simulationat100 rpm. . . . . . . . . . . . . 53

6.18 Test ben h results of the high frequen y inje tion algorithm at 200 rpm starting fromrest, no load. . . . . . . . . . . . . . . . . . . . . . 54

6.19 Test ben hresultsofthe highfrequen y inje tionalgorithmfrom200 to20 rpm atno load. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.20 Testben hresultsofthehighfrequen yinje tionalgorithmat20rpm with load hange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.21 Test ben h results of the high frequen y inje tion algorithm at on- stantload and speed hange. . . . . . . . . . . . . . . . . . . . . . . . 55

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3.1 EKF pro ess table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Base values forthe normalization. . . . . . . . . . . . . . . . . . . . . 19

5.1 Matrix dimensions of the EKF . . . . . . . . . . . . . . . . . . . . . . 37

6.1 Te hni al data of the PMSM. . . . . . . . . . . . . . . . . . . . . . . 45

B.1 Base values equationsfor normalization. . . . . . . . . . . . . . . . . 68

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Introdu tion

Permanent magnet syn hronous ma hines (PMSM) are repla ing the onventional

indu tion ma hine due to the advantages they oer: high e ien y, smaller size,

and faster dynami response [1℄. The only fa tor that might be slowing down the

use of these ma hines is the pri e and availability of the magnetsused. This isdue

to the fa t that the rotor has permanent magnetsinstead of opper windings, and

thesemagnetsaremanufa turedfromrearearthmaterial,whi harenotabundantly

available anywhere and are alwayssubje t topri e hanges.

The ontrol of PMSMhas alsoimproved during the lasttwo de ades. In re ent

years there has been a lot of resear h on the best ontrol strategy to be used.

The two main ontrol s hemes so far are: eld oriented ontrol and dire t torque

ontrol. Ea h s heme oers some advantages and disadvantages, of whi h the the

eld oriented ontrol is the most superior [2℄. New and more advan ed methods

su has predi tive ontrolhave been proposed. Thesemethodsoerfaster response

and less harmoni ontent onthe expense of in reased omplexity [2℄.

The resear h on the design, ontrol, and operation of PMSM is a ontinuing

work with the aim of a hieving higher e ien ies and lower osts, espe ially with

the re ent green poli ies implemented all around the world. There is a general

drive to de rease arbon emissions world wide with many solutions of whi h most

needele tri alma hines: windpower, ele tri ars,highspeed ele tri trains...hen e

thetenden ytoin rease theresear honele tri alma hinesandprovidenewdesigns

and new ontrolmethodsof whi h one is presented inthis report.

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1.1 Motivation

Toperform a proper eld oriented ontrol, the position and speed of the rotor, and

the measured urrents have to be fed ba k from the ma hine. Normally this is

done by a me hani al en oder xed on the shaft of the rotor, and urrent sensors.

Figure 1.1 shows a typi al eld oriented ontrol s heme. The additional en oder

outputsagoodspeedandpositionsignal,ontheexpenseofin reased ost,additional

omplexity, in reasednoise,and redu ed reliabilitydue tothe riskofdamage. Thus

the need rises toremove this sensorand in rease the robustness of the system. The

possibility ofa hieving this goalin reased with the availabilityand improvementof

several dynami state estimators,where itwasshown that itis possibleto estimate

the speed and positionof the rotor using just urrentand voltage measurementsas

input, and themathemati almodelof the ma hine. The termsensorless iswidely

used in literature but a bit ina urate sin e there are still at least urrent sensors

used, whereas the term en oderless more resembles the system. Resear h in the

eld ofsensorless ontrolhasbeengoing onformorethan twenty years, andseveral

su essful methods have been proposed, however industrial implementation is still

slowwithonlyafewtomention[3℄. Thisisbe ausesensorlessmethodshavedierent

performan e for dierent ma hines and speed ranges, and the ompletely robust

oneswhi harereliableandsafeenoughtobeimplementedintheindustryarenotso

ommon. Themaindi ultiespreventing sensorless ontrolfromimplementationin

the industry are: robustness,fun tionalsafety, and hange of behaviouratdierent

loads or speed ranges.

Oneimportantthingto onsiderwhenimplementingasensorless ontrolmethod

is to hoose whether to implement the ontrol system on a Digital Signal Pro es-

sor (DSP) or on a Field Programmable Gate Array (FPGA) platform. The two

platforms have their advantages and disadvantages, all depending on the omplex-

ity of the system. DSP based systems have been used more often due to their low

ost andabilitytoimplement omplexmethodsonthe expense of limitedexe ution

time. FPGA based systems onthe other hand providefaster exe ution time onthe

expense ofhigher ost,and are usually less favored asthe omplexity of the system

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ab abc ab

dq

+-

nref PIn PIq

PId

+-

SVM Inverter

PMSM DC

ab dq idref=0

Encoder

iqref Ua

Ub

i_a ib

q

Figure 1.1: Fieldoriented ontrol.

in reases. In [4℄, the authors have given a omparison between the two platforms

withanappli ationforoneofthesensorless ontrolmethods(theExtendedKalman

Filter). It was found that an FPGA implementation results in an exe ution speed

almostten times faster than aDSP implementation. That being said, the advan e-

ment in FPGA te hnology, and the de rease in pri e show that it ould provide a

better solution inthe eld of sensorless ontrol. One issue remains,and that is the

design pro ess. Traditionally this pro ess starts with the simulation of the algo-

rithm,then writingthe hardware des riptionlanguage, and nallysynthesizingand

downloading the bit stream on the FPGA. This pro ess takes a lot of time and is

prone to errors espe ially as the omplexity of an algorithm su h as the Kalman

lter is high. Thus the motivation to use the model based design (MBD) for FP-

GAs. This approa h de reases the design time, and the possibility of performing a

Hardware-in-the-loop (HIL) test prior to implementation enables testing for ee t

of the FPGA model on the system, whi h is not possible with traditional design

pro esses [5℄. In this proje t, the software Simulink from Mathworks

R

is used to

for simulationusing oatingpointand thenxed point, HDL ode generation,and

hardware-in-the-looptesting.

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1.2 Thesis Outline

Belowabriefoverview ofthethesisisgivenwithashortdes riptionofea h hapter.

In the rst hapter, anintrodu tion tothe proje t is given, followed by a moti-

vationfor the workdone.

Inthese ond hapter, ba kgroundonsensorless ontrolingeneralisintrodu ed,

and a briefintrodu tionto the dierent methods found inliterature.

The third hapter introdu es the Kalam lter and the Extended Kalman lter

algorithm,and the implementationof the lter in sensorless ontrol.

The fourth hapter talks about salien y based methods in generaland the high

frequen y inje tionalgorithm inparti ular.

In the fth hapterthe modelbased design methodology is introdu ed,and the

stages that were followed inthis proje t.

Inthesixth hapter,the simulationandexperimentalresultsareshown withthe

analysis.

The appendix is made of three parts: the list of symbols, the per-unit system,

and xed point data type.